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Article

Damage Detection on a Beam with Multiple Cracks: A Simplified Method Based on Relative Frequency Shifts

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Department of Engineering Sciences, University “Babes-Bolyai” of Cluj-Napoca, Traian Vuia Square, No. 1-4, 320085 Resita, Romania
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IDMEC, Instituto Superior Técnico, University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
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Institute of Research and Development, Duy Tan University, 03 Quang Trung, Da Nang 550000, Vietnam
4
Laboratory Soete, Ghent University, Technologiepark Zwijnaarde 903, B-9052 Zwijnaarde, Belgium
*
Author to whom correspondence should be addressed.
This paper is an extension version of the conference papers Tufisi C., Gillich G.R., Hamat C.O., Manescu T. Study regarding the effect of crack branching on the eigenfrequencies of beams. In Proceedings of the 13th International Conference on Damage Assessment of Structures, Porto, Portugal, 9–10 July 2019 and Gillich, G.R., Aman, A.T., Wahab, M.A., Tufisi, C. Detection of Multiple Cracks Using an Energy Method Applied to the Concept of Equivalent Healthy Beam. In Proceedings of the 13th International Conference on Damage Assessment of structures, Porto, Portugal, 9–10 July 2019.
Academic Editor: Andrea Cataldo
Sensors 2021, 21(15), 5215; https://doi.org/10.3390/s21155215
Received: 23 June 2021 / Revised: 28 July 2021 / Accepted: 30 July 2021 / Published: 31 July 2021
(This article belongs to the Special Issue Data Acquisition and Processing for Fault Diagnosis)
Identifying cracks in the incipient state is essential to prevent the failure of engineering structures. Detection methods relying on the analysis of the changes in modal parameters are widely used because of the advantages they present. In our previous research, we found that eigenfrequencies were capable of indicating the position and depth of damage when sufficient vibration modes were considered. The damage indicator we developed was based on the relative frequency shifts (RFS). To calculate the RFSs for various positions and depths of a crack, we established a mathematical relation that involved the squared modal curvatures in the healthy state and the deflection of the healthy and damaged beam under dead mass, respectively. In this study, we propose to calculate the RFS for beams with several cracks by applying the superposition principle. We demonstrate that this is possible if the cracks are far enough from each other. In fact, if the cracks are close to each other, the superposition method does not work and we distinguish two cases: (i) when the cracks affect the same beam face, the frequency drop is less than the sum of the individual frequency drops, and (ii) on the contrary, cracks on opposite sides cause a decrease in frequency, which is greater than the sum of the frequency drop due to individual damage. When the RFS curves are known, crack assessment becomes an optimization problem, the cost function being the distance between the measured RFSs and all possible RFSs for several vibration modes. Thus, the RFS constitutes a benchmark that characterizes damage using only the eigenfrequencies. We can accurately locate multiple cracks and estimate their severity through experiments and thus prove the reliability of the proposed method. View Full-Text
Keywords: damage detection: multi-cracked beam; eigenfrequency; deflection; superposition damage detection: multi-cracked beam; eigenfrequency; deflection; superposition
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MDPI and ACS Style

Gillich, G.-R.; Maia, N.M.M.; Wahab, M.A.; Tufisi, C.; Korka, Z.-I.; Gillich, N.; Pop, M.V. Damage Detection on a Beam with Multiple Cracks: A Simplified Method Based on Relative Frequency Shifts. Sensors 2021, 21, 5215. https://doi.org/10.3390/s21155215

AMA Style

Gillich G-R, Maia NMM, Wahab MA, Tufisi C, Korka Z-I, Gillich N, Pop MV. Damage Detection on a Beam with Multiple Cracks: A Simplified Method Based on Relative Frequency Shifts. Sensors. 2021; 21(15):5215. https://doi.org/10.3390/s21155215

Chicago/Turabian Style

Gillich, Gilbert-Rainer, Nuno M.M. Maia, Magd A. Wahab, Cristian Tufisi, Zoltan-Iosif Korka, Nicoleta Gillich, and Marius V. Pop 2021. "Damage Detection on a Beam with Multiple Cracks: A Simplified Method Based on Relative Frequency Shifts" Sensors 21, no. 15: 5215. https://doi.org/10.3390/s21155215

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